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arXiv · 0804.3566

Derivation of a Vacuum Refractive Index in a Stringy Space-Time Foam Model

John Ellis·N. E. Mavromatos·D. V. Nanopoulos
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Abstract

It has been suggested that energetic photons propagating in vacuo should experience a non-trivial refractive index due to the foamy structure of space-time induced by quantum-gravitational fluctuations. The sensitivity of recent astrophysical observations, particularly of AGN Mk501 by the MAGIC Collaboration, approaches the Planck scale for a refractive index depending linearly on the photon energy. We present here a new derivation of this quantum-gravitational vacuum refraction index, based on a stringy analogue of the interaction of a photon with internal degrees of freedom in a conventional medium. We model the space-time foam as a gas of D-particles in the bulk space-time of a higher-dimensional cosmology where the observable Universe is a D3-brane. The interaction of an open string representing a photon with a D-particle stretches and excites the string, which subsequently decays and re-emits the photon with a time delay that increases linearly with the photon energy and is related to stringy uncertainty principles. We relate this derivation to other descriptions of the quantum-gravitational refractive index in vacuo.

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John Ellis, N. E. Mavromatos, D. V. Nanopoulos. 2008-04-22. Derivation of a Vacuum Refractive Index in a Stringy Space-Time Foam Model. https://doi.org/10.1016/j.physletb.2008.06.029

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